Superconducting p-branes and Extremal Black Holes

In Einstein-Maxwell theory, magnetic flux lines are `expelled' from a black hole as extremality is approached, in the sense that the component of the field strength normal to the horizon goes to zero. Thus, extremal black holes are found to exhibit the sort of `Meissner effect' which is characteristic of superconducting media. We review some of the evidence for this effect, and do present new evidence for it using recently found black hole solutions in string theory and Kaluza-Klein theory. We also present some new solutions, which arise naturally in string theory, which are non-superconducting extremal black holes. We present a nice geometrical interpretation of these effects derived by looking carefully at the higher dimensional configurations from which the lower dimensional black hole solutions are obtained. We show that other extremal solitonic objects in string theory (such as p-branes) can also display superconducting properties. In particular, we argue that the relativistic London equation will hold on the worldvolume of `light' superconducting p-branes (which are embedded in flat space), and that minimally coupled zero modes will propagate in the adS factor of the near-horizon geometries of `heavy', or gravitating, superconducting p-branes.Comment: 22 pages, 2 figure

Nonexistence of marginally trapped surfaces and geons in 2+1 gravity

We use existence results for Jang's equation and marginally outer trapped surfaces (MOTSs) in 2+1 gravity to obtain nonexistence of geons in 2+1 gravity. In particular, our results show that any 2+1 initial data set, which obeys the dominant energy condition with cosmological constant \Lambda \geq 0 and which satisfies a mild asymptotic condition, must have trivial topology. Moreover, any data set obeying these conditions cannot contain a MOTS. The asymptotic condition involves a cutoff at a finite boundary at which a null mean convexity condition is assumed to hold; this null mean convexity condition is satisfied by all the standard asymptotic boundary conditions. The results presented here strengthen various aspects of previous related results in the literature. These results not only have implications for classical 2+1 gravity but also apply to quantum 2+1 gravity when formulated using Witten's solution space quantization.Comment: v3: Elements from the original two proofs of the main result have been combined to give a single proof, thereby circumventing an issue with the second proof associated with potential blow-ups of solutions to Jang's equation. To appear in Commun. Math. Phy